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Non resonant atom photoionization by intense fields with Raman processes
Volume 45A, number 2
10 September
PHYSICS LETTERS
1973
NON RESONANT ATOM PHOTOIONIZATION BY INTENSE FIELDS WITH RAMAN PROCESSES A. RACHMAN, G. LARLANCHE and M. JAOUEN Faculte’des Sciences, Laboratoire de Physique du Laser, 86022 Poitiers, France Received 5 April 1973 Multiphoton ionization by strong fields of hydrogenlike atoms is analyzed from the stand-point of a non perturbative theory introducing generalized Raman processes. The transition amplitude for N-photon absorption is obtained and applied to the case of non-resonant one-photon ionization; significant departures from perturbation theory calculations are predicted.
In the interaction of strong electromagnetic fields with atoms complicated processes may appear as a result of the effect of the field on the bound states of the electron in the atom. Certain experiments report multiphoton ionization by laser action supposed to occur through resonances where resonant levels were assumed to beStark shifted over tenths of angstroms [ 1,2] attempting to explain resonance detuning relative to an integer multiple of the laser photon energy. Other experiments on the same subject using tunable lasers report the surprising feature that the apparent number of quanta absorbed in the multiphoton ionization process is greater than the theoretical value k, calculated on the basis of energy conservation [3,4] ; moreover the difference k, oscillates as a function of the laser k = km,frequency changing its sign and significient departures from the k, value have been observed. Attentive inspection of paper [3 ] shows that multiphoton absorption by tunable lasers occurs apparently in most cases through non resonant processes. In ref. [5] it is predicted that under the action of intense fields the average energy of an atom oscillates in phase with the applied electric field, with the same amplitude as if that field were static. Then we may conclude that the behaviour of atoms under the action of strong fields is completely different from that one related to the presence of low intensity fields; caution must be exercised in the application of perturbation methods when intense fields are present. In this letter we report a theoretical analysis of nonresonant multiphoton absorption based on the non perturbative semi-classical momentum translation method [S, 61 using the T-matrix formalism for
transitions and then introducing weak field generalized Raman processes [5,7]. We may account for multiphoton absorption by non resonant interactions through N absorbed photons from the intense field plus the absorption or emission of one Raman photon. The introduction of these processes allows the fulfillment of the condition o(Ei-Ef)-’ .eauo Q 1 [ 51 even for a small number of absorbed photons from the strong field. The T-matrix element between two atomic states pi and #f [5] for the N photon absorption from the strong field plus the absorption of one
Fig. 1.
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Volume 45A, number 2
PHYSICS LETTERS
Fig. 2. Raman photon is given by 7$y1) = $iN”(Ei-Ef)
exp(*ia)
ea*
where JN is the Nth order Bessel function of first kind, a and a^are the intense and weak field vector potential amplitudes respectively, X the electron radius vector, E the intense electromagnetic field polarisation unit vector, g the same vector for the weak field, Ei and E, the energies for the initial and final states pi and @, OLthe displacement in phase between the weak and the strong field. We consider an s electron final state of the continuum spectrum and the 1s initial state of the discrete spectrum and linearly polarized light. If we take N = 2j t 1 we obtain for the reduced amplitude transition [5]
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10 September 1973
with 0 = (1 - &u,)~ and B = 1 t Y2/& a, is the Bohr radius, Y = eaa, fixes the laser beam intensity, k the momentum of the ejected electron. Let us now study the transition amplitude for one-photon ionization under the action of the strong field. We represent Z(l) =f( Y) in fig. 1 for different values of the k parameter i.e. for different values of the energy of the ejected electron equal to E, = *ET, &ET, &ET where ET is the energy of the 1s level of the discrete spectrum of hydrogen. We note that when Y increases fr.om zero, i!l) increases till certain value of Y and then decreases towards zero when Y goes towards infinite, a result not to be expected from usual perturbation theory. It appears significant also to represent Z(l) versus the k momentum for fixed Y values (fig. 2) (Y = 1 corresponds to about 1.5 X 1014W/cm2 or 1.06pm radiation). The obtained set of curves begins with 0 fork = 0, they show oscillations, and finally go towards 0 with increasing k via one or several k values where the transition amplitude vanishes, fact that means a zero for the transition probability. Such results are not to be expected from usual perturbation methods; we wish to outline that a significant dip of the ionization probability (antiresonance) as a function of the laser frequency has been lately observed in multiphoton ionization experiments using tunable lasers [3]. For the intensity Y = 10, the transition amplitude almost vanishes (fig. 2); this would mean that at such laser intensity high order processes may be more probable.
References [l] R.G. Evans and P.C. Thonemann, Phys. Lett. 39A (1972) [2] [3] [4] [5] [6] [7]
133. J. Bakos et al., Phys. Lett. 41A (1972) 163.. B. Held et al., Phys Rev. Lett. 30 (1973) 423. J. Bakos et al., Phys. Lett. 39A (1972) 283. H.R. Reiss, Phys. Rev. Al (1970) 803. H.R. Reiss, Phys. Rev. D4 (1971) 3533. Man Mohan and R.K. Thareja, Phys. Rev. A7 (1973) 34.
10 September
PHYSICS LETTERS
1973
NON RESONANT ATOM PHOTOIONIZATION BY INTENSE FIELDS WITH RAMAN PROCESSES A. RACHMAN, G. LARLANCHE and M. JAOUEN Faculte’des Sciences, Laboratoire de Physique du Laser, 86022 Poitiers, France Received 5 April 1973 Multiphoton ionization by strong fields of hydrogenlike atoms is analyzed from the stand-point of a non perturbative theory introducing generalized Raman processes. The transition amplitude for N-photon absorption is obtained and applied to the case of non-resonant one-photon ionization; significant departures from perturbation theory calculations are predicted.
In the interaction of strong electromagnetic fields with atoms complicated processes may appear as a result of the effect of the field on the bound states of the electron in the atom. Certain experiments report multiphoton ionization by laser action supposed to occur through resonances where resonant levels were assumed to beStark shifted over tenths of angstroms [ 1,2] attempting to explain resonance detuning relative to an integer multiple of the laser photon energy. Other experiments on the same subject using tunable lasers report the surprising feature that the apparent number of quanta absorbed in the multiphoton ionization process is greater than the theoretical value k, calculated on the basis of energy conservation [3,4] ; moreover the difference k, oscillates as a function of the laser k = km,frequency changing its sign and significient departures from the k, value have been observed. Attentive inspection of paper [3 ] shows that multiphoton absorption by tunable lasers occurs apparently in most cases through non resonant processes. In ref. [5] it is predicted that under the action of intense fields the average energy of an atom oscillates in phase with the applied electric field, with the same amplitude as if that field were static. Then we may conclude that the behaviour of atoms under the action of strong fields is completely different from that one related to the presence of low intensity fields; caution must be exercised in the application of perturbation methods when intense fields are present. In this letter we report a theoretical analysis of nonresonant multiphoton absorption based on the non perturbative semi-classical momentum translation method [S, 61 using the T-matrix formalism for
transitions and then introducing weak field generalized Raman processes [5,7]. We may account for multiphoton absorption by non resonant interactions through N absorbed photons from the intense field plus the absorption or emission of one Raman photon. The introduction of these processes allows the fulfillment of the condition o(Ei-Ef)-’ .eauo Q 1 [ 51 even for a small number of absorbed photons from the strong field. The T-matrix element between two atomic states pi and #f [5] for the N photon absorption from the strong field plus the absorption of one
Fig. 1.
155
Volume 45A, number 2
PHYSICS LETTERS
Fig. 2. Raman photon is given by 7$y1) = $iN”(Ei-Ef)
exp(*ia)
ea*
where JN is the Nth order Bessel function of first kind, a and a^are the intense and weak field vector potential amplitudes respectively, X the electron radius vector, E the intense electromagnetic field polarisation unit vector, g the same vector for the weak field, Ei and E, the energies for the initial and final states pi and @, OLthe displacement in phase between the weak and the strong field. We consider an s electron final state of the continuum spectrum and the 1s initial state of the discrete spectrum and linearly polarized light. If we take N = 2j t 1 we obtain for the reduced amplitude transition [5]
156
10 September 1973
with 0 = (1 - &u,)~ and B = 1 t Y2/& a, is the Bohr radius, Y = eaa, fixes the laser beam intensity, k the momentum of the ejected electron. Let us now study the transition amplitude for one-photon ionization under the action of the strong field. We represent Z(l) =f( Y) in fig. 1 for different values of the k parameter i.e. for different values of the energy of the ejected electron equal to E, = *ET, &ET, &ET where ET is the energy of the 1s level of the discrete spectrum of hydrogen. We note that when Y increases fr.om zero, i!l) increases till certain value of Y and then decreases towards zero when Y goes towards infinite, a result not to be expected from usual perturbation theory. It appears significant also to represent Z(l) versus the k momentum for fixed Y values (fig. 2) (Y = 1 corresponds to about 1.5 X 1014W/cm2 or 1.06pm radiation). The obtained set of curves begins with 0 fork = 0, they show oscillations, and finally go towards 0 with increasing k via one or several k values where the transition amplitude vanishes, fact that means a zero for the transition probability. Such results are not to be expected from usual perturbation methods; we wish to outline that a significant dip of the ionization probability (antiresonance) as a function of the laser frequency has been lately observed in multiphoton ionization experiments using tunable lasers [3]. For the intensity Y = 10, the transition amplitude almost vanishes (fig. 2); this would mean that at such laser intensity high order processes may be more probable.
References [l] R.G. Evans and P.C. Thonemann, Phys. Lett. 39A (1972) [2] [3] [4] [5] [6] [7]
133. J. Bakos et al., Phys. Lett. 41A (1972) 163.. B. Held et al., Phys Rev. Lett. 30 (1973) 423. J. Bakos et al., Phys. Lett. 39A (1972) 283. H.R. Reiss, Phys. Rev. Al (1970) 803. H.R. Reiss, Phys. Rev. D4 (1971) 3533. Man Mohan and R.K. Thareja, Phys. Rev. A7 (1973) 34.